Sunday, September 16, 2012

A Treatise on the Family

Gary Becker, a Nobel laureate economist, analyzed marriage, births, divorce, division of labor in households, inequality, altruism and other nonmaterial behavior with the tools and framework developed for material behavior, i.e. economics. His purpose was to develop a rational choice approach to the family. In his book, “A Treatise on the Family”, Becker used basic tools of economics and derived conclusions, some of which may sound counter-intuitive.

Division of labor
Becker analyzes division of household labor in chapter 2 of the book. He argues that even if a husband and wife are intrinsically identical, they gain from a division of labor between market and household activities, with one of them specializing more in market activities and the other specializing more in household activities. What he introduced to derive the conclusion is the concept of relative advantage and human capital investment. The followings are the theorems in chapter 2 (page 33 to 36):

Theorem 2.1. If all members of an efficient household have different comparative advantages, no more than one member would allocate time to both the market and household sectors. Everyone with a greater comparative advantage in the market than this member’s would specialize completely in the market, and everyone with a greater comparative advantage in the household would specialize completely there.

Theorem 2.2. If all members of a household have different comparative advantages, no more than one member would invest in both market and household capital. Members specializing in the market sector would invest only in market capital, and members specializing in the household sector would invest only in household capital.

Theorem 2.3. At most one member of an efficient household would invest in both market and household capital and would allocate time to both sectors.

Theorem 2.4. If commodity production functions have constant or increasing returns to scale, all members of efficient households would specialize complete in the market or household sectors and would invest only in market or household capital.

These theorems would explain the fact that in many families, there is division of labor to some extent, and in some cases those who spend time for market labor also do for household labor as well. Becker’s statement also shows us that why the labor division is made based on sexual differences – it is because only a slight difference leads to division of labor and once the division is made, the comparative advantages of family members would get fixed. Note, however, that Becker did not say that biological difference is the sole reason of labor division, or “exploitation of household women”.  

Becker also mentions about the recent trends in women’s labor force participation rates, fertility, and divorce rates. The rapid expansion of the service sector enabled more women to participate into market labors. Thus, “the growth in the earning power of married women raised the forgone value of their time spent at child care and other household activities, which in turn reduced the demand for children and encouraged a substitution away from parental, especially mothers’ time. Both of these changes raised the labor force participation of married women. The gain from marriage is reduced, and hence the attractiveness of divorce is raised, by higher earnings and labor force participation of married women, because the sexual division of labor within household becomes less advantageous.” (page 55)  The same can be said for the women in the course of economic independence in developing countries.

Competition in marriage market
Chapter 3 and 4 analyze the competition for marriage partners among men and women of different incomes, abilities, education ages, family backgrounds, and other attributes.

An efficient marriage market develops “shadow” prices to guide participants to marriages that will maximize their expected well-being. These prices, central to the analysis in this chapter and the subsequent one, are responsible for the more powerful implications.

The general concept of marriage in Becker’s model is that marriage increases output of both male and female, and the marginal increase of output from an additional husband/wife is positive. In this setup, polygamy is more beneficial for both male and female, if either men or women differ significantly in efficiency (ability to generate output), or if the ratio of eligible men to eligible men and eligible women differ significantly, the conclusion that is analogous to the efficient use of resources.

Becker’s model explains under what situation people would invest more in superior skill (the skill that makes one attractive), e.g. having education, training, etc. Becker argues that, when the marginal contribution of women/men to output is greater, people have more incentive to invest to increase their efficiency. Usually, polygamy increases the expected marginal increase of output, as men/women can choose more than one mate.

This model suggests explanation of why polygyny is more common than polyandry. The situation originally begins with a small difference. If the marginal contribution of women is larger, that incentivizes men to invest more in their skills and women to invest less (as they have more expected opportunity to get married), and that raises the average efficiency and the inequality in efficiency of men relative to women. The difference of contribution for output may be coming from biological difference. Becker said that both average and standard deviation of years of schooling are usually much lower for women than men in poor countries with monogamous marriages, where presumably the marginal contribution of women to output is greater than the marginal contribution of men because of the value of having many children. (page 104)

Becker then analyzes assortative mating using the same framework. He says that correlations between intelligence, education, age, race, nonhuman wealth, religion, ethnic origin, height, place of origin, and many other traits of spouses are positive and strong. Especially the correlation between spouses by intelligence is strong – it is as high as that between siblings. On the other hand, persons who marry out of their race, religion, age cohort, or education class have relatively high probabilities of divorce, even when other traits are held constant. (page 117-118)

Becker argues that preferences could well affect the equilibrium sorting if costs were no the same in all households. For example, persons with similar preferences have an incentive to marry each other if costs are lower when the consumption patterns of mates are more similar, as they would be when some commodities are jointly consumed, when production of commodities is more efficient at a larger scale, or when specialized consumption capital lowers the costs of particular commodities. (page 123)

Love can also be understood in Becker’s framework. Love can be defined such that her/his welfare enters his/her utility function or that he/she values emotional and physical contact with her/him.

The demand for children
Becker applied the same economic framework to fertility.

One factor deeply affecting child birth rate is children’s future productivity. In the past, there was more child birth in suburban area, because having more children was more productive on farms than in cities. The reason is that agriculture in the past did not require any complex labor, and thus children at young age can contribute to enhance a family’s productivity. The contribution of farm children has declined as agriculture has become more mechanized and complex in the course of economic development.

Second factor is the value of the time of married women, because the cost of the mother’s time is a major part of the total cost of producing and rearing children. The number of children is strongly negatively related to the wage rate or other measures of the value of time of wives. Becker said that the growth in the earning power of women during the last hundred years in developed countries is a major cause of both the large increase in labor force participation of married women and the large decline in fertility. (page 140)

Third factor is education and the number of children. There are negative correlation between the number of children and the quality of education for them (see the table below). Becker points out that Jewish families have been smaller than average over the last 150 years and have invested more in human capital, and in recent decades they have had higher incomes.

Country and period
Change in
birth rate
Change in schooling
US 1920 -1930
US 1960 – 1972
Japan 1950-1960
Taiwan 1960 – 1975
England & Wales 1871-1901

Becker also points out that government programs significantly affected child birth rate. The recent increase in fertility rate in France would be a good example to show that families would respond to the monetary incentives in deciding the number of children.

Inequality and Intergenerational Mobility
Becker also analyzes inequality. He argues that even if all families were basically identical, incomes would be unequally distributed because of the unequal incidence of endowment and market luck. The inequality prevails over generations, as lucky parents invest more in their children, and the increase in the children’s incomes would induce them to invest more in their own children in the succeeding generation, and soon until all descendants benefit from the initial luck (page 203). Moreover, Children’s incomes are linked to their parents not only through investments but also through such endowments as reputation, connections, knowledge, skills, goals provided by their family environment, genetically determined race and other characteristics.

Becker’s argument about intergenerational mobility assumes that parents feel better if their children are better off, i.e. the utility function of parents are made of both their own income and the quality of children. Becker analyzes the altruism in the family in this book as well. According to Becker, “altruistic” means that one’s utility function depends positively on the well-being of others.

Say an altruist is the mother of a family and has several beneficiaries, including children, spouses, parents and siblings. Becker analyzes the situation more profoundly and proposes an interesting theorem (page 288):

Rotten Kid Theorem: Each beneficiary, no matter how selfish, maximizes the family income of his benefactor and thereby internalizes all effects of his actions on other beneficiaries.

Corollary: Each beneficiary, no matter how envious of other beneficiaries or of his benefactor, maximizes the family income of the benefactor, and hence helps those envied.

It is surprising to see that the economic model of this book well describes the behavior of family to the large extent. Human beings may not be rational as an individual but may be very rational as a group, and frameworks of economics are very powerful tool to analyze the situation (sometimes they reveal uncomfortable truth though). That is why I believe to learn economics is valuable for everyone even for those who don’t care about economy.

Gary Becker, “A Treatise on the Family”, Harvard University Press (Enlarged edition), 1993/10/15

No comments: